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integrate sin2x/sin5xsin3x

integrate sin2x/sin5xsin3x

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

sin2x can be written as sin(5x-3x)=sin5xcos3x-sin3xcos5x

   sin2x/sin5x.sin3x=sin5xcos3x-sin3xcos5x/sin5xsin3x

   =cot3x-cot5x

  integral of cot3x-cot5x=logsin3x/3  -  logsin5x/5 + c

                                  =log{(sin3x)^1/3/(sin5x)^1/5} + c

 

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